# 1933

This number is a prime.

In January 1933 Adolf Hitler was appointed chancellor of Germany and before August of the same year Germany was declared a one-party state.

The smallest prime (emirp) whose the sum and the product of digits are equal to the same powers of consecutive primes (16=2^4, 81=3^4). Note that the sum plus the product of these digits is equal to the largest double-digit prime (emirp). [Loungrides]

The only year of the 20th century to divide a repunit prime with no more than 21 digits: 111111111111111111111 = 3 * 37 * 43 * 239 * 1933 * 4649 * 10838689. It therefore divides the repunit prime with 2*21 = 42 digits. [Post]

Inauguration Day in the United States occurred on March 4 from 1798 up to the emirp year 1933 when Franklin D. Roosevelt was inaugurated President. Since then Inauguration Day has been on January 20. Furthermore, 3041933 (3/04/1933) is prime. [Green]

1933 = (1^{9} + 2^{8} + 3^{7} +
4^{6} + 5^{5})/5. [Wesolowski]

The smallest happy balanced prime. [Gaydos]

The smallest Honaker prime with a Sophie Germain prime twin. [Gaydos]

1933 is the smallest prime whose sum of each digit raised to the same whole number is square. [Gaydos]

9331 is the smallest positive integer whose sum of divisors (1933) is its prime anagram. [Gaydos]

The smallest prime obtained by concatenating all (unordered) pairs whose product is a given number (9 in this case): 1•9=3•3. [Leonardis]

Stanley Skewes in 1933 (assuming the Riemann Hypothesis) was the first to give an explicit upper bound for Ξ. [Plymen]